The Mutual Information is a measure of the similarity between two labels of
the same data. Where \(|U_i|\) is the number of the samples
in cluster \(U_i\) and \(|V_j|\) is the number of the
samples in cluster \(V_j\), the Mutual Information
between clusterings \(U\) and \(V\) is given as:

This metric is independent of the absolute values of the labels:
a permutation of the class or cluster label values won’t change the
score value in any way.

This metric is furthermore symmetric: switching label_true with
label_pred will return the same score value. This can be useful to
measure the agreement of two independent label assignments strategies
on the same dataset when the real ground truth is not known.